Topological fixed point theorems do not hold for random dynamical systems (Q1961330)

The main goal of the authors is to know, whether it is possible to generalize topological fixed point theorems to the case of random dynamical systems, which means that under reasonable assumptions every continuous random dynamical systems on the closed unit ball in \(\mathbb{R}^d\) has a random invariant point. The authors prove that there do not exist canonical generalizations of this theorem. To this end the authors use tools from algebraic ergodic theory.